| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Differential Equations | BM221 | 3. Semester | 4 + 0 | 4.0 | 4.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Face to face education |
| Course Coordinator |
Assist. Prof. Dr. Barış KANTOĞLU |
| Instructor(s) | |
| Assistants | |
| Goals | Matematiksel düşünceyi geliştirmek. Matematik, Fizik ve mühendislikte karşılaşılan diferansiyel denklem problemlerini çözebilmek. |
| Course Content | Diferansiyel denklemlerin temel kavramları ve çeşitli mühendislik alanlarında uygulamaları. Birinci mertebeden diferansiyel denklemlerin sınıflandırılması, Birinci mertebeden değişkenlerine ayrılabilir diferansiyel denklemler. Homojen diferansiyel denklemler. Homojen türe dönüştürülebilen diferansiyel denklemler. Tam diferansiyel denklemler. Tam diferansiyel türe dönüştürülebilen diferansiyel denklemler. Birinci mertebeden lineer diferansiyel denklemlerin mühendislik uygulamaları ve çözümler teorisi. Bernoulli diferansiyel denklemi. Riccati diferansiyel denklemi. Yüksek dereceden diferansiyel denklemler. Clairaut diferansiyel denklemi. Lagrange diferansiyel denklemi. İkinci mertebeden diferansiyel denklemler. İkinci mertebeden lineer diferansiyel denklemler. |
| Learning Outcomes |
- Diferansiyel denklemi tanımlar - Değişkenlerine ayrılabilen, homojen, lineer, tam diferansiyel denklem çeşitlerini çözer - Bernoulli ve Riccati diferansiyel denklemlerini çözer - İkinci ve daha yüksek mertebeden sabit katsayılı lineer diferansiyel denklemleri çözer - Yüksek dereceden diferansiyel denklemleri çözer. - Parametrelerin değişimi yöntemini bilir. - Değişken katsayılı diferansiyel denklemleri tanımlar - Bazı değişken katsayılı diferansiyel denklemleri çözer |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Basic concepts and classification of differential equations | Verbal Expression Course Hours Practice Visual Presentation |
| 2. Week | Introduction to first order differential equations, differential equations that can be divided into variables | Visual Presentation Verbal Expression Practice Course Hours |
| 3. Week | Linear Differential Equations | Practice Visual Presentation Verbal Expression Course Hours |
| 4. Week | Homogeneous Differential Equations | Practice Course Hours Verbal Expression Visual Presentation |
| 5. Week | Exact Differential Equations | Course Hours Visual Presentation Verbal Expression Practice |
| 6. Week | Fully Differential Equation Convertible Differential Equations | Verbal Expression Visual Presentation Practice Course Hours |
| 7. Week | Bernoulli and Riccati Differential Equations | Course Hours Practice Verbal Expression Visual Presentation |
| 8. Week | Bernoulli and Riccati Differential Equations | |
| 9. Week | Engineering applications and solutions theory of first order differential equations. | Course Hours Verbal Expression Practice Visual Presentation |
| 10. Week | High order differential equations, Lagrange and Clairaut differential equations | Visual Presentation Course Hours Practice Verbal Expression |
| 11. Week | Introduction to higher order differential equations, differential equations with constant coefficients | Verbal Expression Course Hours Practice Visual Presentation |
| 12. Week | Differential equations with variable coefficients | Course Hours Verbal Expression Practice Visual Presentation |
| 13. Week | Differential equations with variable coefficients | Visual Presentation Practice Verbal Expression Course Hours |
| 14. Week | Method of variation of parameters | Practice Visual Presentation Course Hours Verbal Expression |
| Yunus A. Çengel ve William J. Palm, Mühendislik ve Temel Bilimler İçin Diferansiyel Denklemler, İzmir Güven Kitabevi 2013. |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | DK7 | DK8 | Measurement Method |
|---|---|---|---|---|---|---|---|---|---|---|
| PY1 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | - |
| PY2 | 5 | 4 | 4 | 4 | 4 | 4 | 2 | 3 | 4 | - |
| PY3 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | - |
| PY4 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | - |
| PY5 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | - |
| PY6 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | - |
| PY7 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | - |
| PY8 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | - |
| PY9 | 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | - |
| PY10 | 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | - |
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Course Hours | 14 | 4 | 56 |
| Midterm 1 | 1 | 1.5 | 1.5 |
| Final | 1 | 1.5 | 1.5 |
| Practice End-Of-Term | 11 | 3 | 33 |
| Classroom Activities | 10 | 1 | 10 |
| Total Workload | 102 | ||
| ECTS Credit of the Course | 4.0 | ||
